This invention relates generally to detecting targets, and more particularly, to methods and systems for locating and characterizing targets using magnetic gradiometry.
Military installations have artillery bombing ranges for target practice. Most of the bombs explode, however some may not and they bury themselves upon impact. Many military installations are to be closed or have been closed and the land will eventually be returned to the public. Disposing of unexploded ordnance involves locating, identifying, excavating and physically removing the ordnance.
Most of the unexploded ordnance removal cost is incurred during excavating as a result of inaccurate ordnance identifications. Ferromagnetic metal objects have strong magnetic fields. Because most ordnance is fabricated from ferromagnetic metal, unexploded ordnance is/are magnetic objects having magnetic fields. Locating magnetic objects of unknown properties involves determining six unknown quantities: three representing the object's location, and three representing its vector magnetic moment. The magnetic gradient tensor includes only five independent quantities. One of Maxwell's Equations is ∇·B=0 everywhere, so the tensor is traceless. Another of Maxwell's Equations reduces to ∇×B=0 in free space, so the tensor is symmetric. In the preceding equations B represents the magnetic field, ∇· represents the divergence of the magnetic field vectors and ∇× represents the curl of the magnetic field vectors. Thus, of the nine available tensor elements, four are redundant and five are independent. So, a single tensor gradiometer measurement is inadequate for determining all six unknowns. Using current techniques, the bearing to an object may be determined, but the moment and magnitude of the object are inextricable, so that a nearby small object cannot be distinguished from a distant large one. Furthermore, using current techniques, the symmetry of the dipole gradient means that there are four mathematical bearing solutions, one of which is the actual bearing and the others of which are so-called “ghost” solutions.
The inversion of magnetic tensor gradient data, regardless of which algorithm is used, yields four equally feasible pairs of solutions. There are magnetically degenerate special cases that have two equally feasible solutions, where each degenerate solution is found twice. Each of the four solutions includes a direction vector from a sensor, or the centroid of an array of sensors known as a gradiometer, toward the dipole position, and an orientation vector for the axis of the magnetic dipole. These can be considered as two pairs of solutions, where each pair has its two positions on opposite sides of the sensor, or gradiometer, and its dipoles pointing in opposite directions. That is, each pair is symmetric via reflection through the origin where the origin defines the sensor, or gradiometer, location.
Several methods determine which pair of solutions is the most likely, namely: geometric; moment magnitude; moment orientation; and kinetics. The geometric method requires that the solution not be underground, not be more than two meters in the air, not be behind the sensor or not experience some other constraint that may be derived from the situation. Using the moment magnitude method, a solution which is not the actual one implies the presence of materials whose magnetic properties are not physically available, or unlikely in the situation. With the moment orientation method, if the object is known to be magnetically permeable with negligible remnant moment, the dipole axis is aligned with the earth's magnetic field. Using the kinetics method, the track of positions over time implies feasible speeds and accelerations. None of these methods is generally valid for all situations because each of them relies on particular criteria that correspond to a given application, deployment, or situation.
There are many situations where the geometric, moment magnitude, moment orientation and kinetics methods are inapplicable and/or insufficient. For example, dipole orientation cannot be used for objects whose remnant magnetization exceeds the induced magnetization. Similarly, the geometric method cannot be used to eliminate a hemisphere when a target can be on either side of the sensor. Although the four pairs of solutions equivalently satisfy the constraints of the tensor gradient data, there are three additional constraint values available from the magnetic field vector.
The first constraint, corresponding to the magnitude of the magnetic field due to the dipole, is independent of the four pairs of solutions. The first constraint serves to scale the four normalized orientation (or bearing) vectors, and the corresponding normalized dipole vectors, to have the correct positional range and magnetic dipole moment.
The second constraint unambiguously selects one solution from each pair. Reversing the orientation of the dipole changes the sign of both the gradient and the magnetic field, but reversing the orientation (or bearing) vector only changes the sign of the gradient, not the magnetic field. Consequently, if the magnetic field vector is computed for each of the two solutions in a pair, one of the computed vectors will be similar to the measured magnetic field vector and the other will be approximately reversed. The solution corresponding to the non-reversed magnetic field vector is the desired solution in any pair of tracking solutions.
The final constraint is used to choose from among the two remaining solution candidates by inspecting those measured and computed magnetic field vectors more closely. One of the two computed magnetic field vectors will correspond more closely, in direction, with the actual magnetic field vector for the dipole than the other vector. Generally, the magnetic field vector corresponding more closely with the actual magnetic field vector direction corresponds to the desired solution. In the presence of significant measurement noise, notably correlated noise, statistical techniques can be used to infer the confidence values for the two solution options.
Magnetic field gradiometers measure the spatial derivatives, ∂/∂xi, where i=1,2,3, of each vector component Bj, where j=1,2,3, of the ambient magnetic field. In the exemplary embodiment, the ambient magnetic field is simply that of the earth. However, it should be appreciated that in various other exemplary embodiments the ambient magnetic field may be an artificially generated field, or in spaceborne uses, the ambient field of the sun or another planet. Because there are three magnetic field components, each of which can be differentiated in three directions, the full gradient is a 3×3 tensor having nine components ∂Bj/∂x. Magnetic field gradiometers used in non-conducting environments have constraints imposed by Maxwell's equations so that not all of the nine tensor components need be measured. Consequently, in most circumstances, only five of the nine tensor components are independent of one another and the other four tensor components can be computed using the five independent tensor components. Maxwell's Equation ∇·B=0 means that the tensor has a zero trace, so that any one of the diagonal terms is the negative of the sum of the other two. In free space, where there is zero electric current, another of Maxwell's Equations reduces to ∇×B=0, which means that the tensor is symmetric: that is for i≠j, ∂Bi/∂xj=∂Bj/∂xi.
FIG. 1 shows a configuration of magnetic sensors used for measuring approximations to the five independent components of the gradient tensor. In the exemplary embodiment three sensing elements, or magnetometer sensors 12, 14, 16, are arranged in an array to form a triangular sensing system configuration defining a gradiometer 10 having an equilateral triangular shape. Each of the magnetometers 12, 14, 16 operates digitally and may be internally controlled using a digital signal processor (DSP) or field programmable gate array (FPGA). Because the magnetometers 12, 14, 16 operate digitally, the output data is in digital form rather than analog form. Additionally, each of the magnetometers 12, 14, 16 is disposed in a vertex of the equilateral triangular gradiometer 10 and measures the magnetic field components Bx, By, Bz, where the z-axis is oriented to come out of the page. Each side of the equilateral triangular gradiometer 10 has a length L. Using the centroid 18 of the equilateral triangular gradiometer 10 as the origin for computations, the coordinates of the center of the three magnetometers 12, 14, 16 are (−L/2, −L/2(3)1/2), (L/2, −L/2(3)1/2), and (0, L/(3)1/2), respectively. The magnetic field measured at each vertex, k, is denoted as kB, with components kBx, kBy, and kBz where k corresponds to the appropriate magnetometer 12, 14, 16.
FIG. 2 shows the Bx, By, Bz components of the magnetic field B measured by each magnetometer 12, 14, 16 disposed at each vertex k. It should be appreciated that at least three magnetometers should be included in the gradiometer 10. Additionally, it should be appreciated that the magnetometers 12, 14, 16 may not lie along the same line because this type of configuration also yields inadequate data for practicing the invention. The three magnetometers 12, 14, 16 may be arranged in any triangular configuration as long as the length, L, of each side of the triangular gradiometer 10 is accounted for. It should be further appreciated that more than three magnetometers 12, 14, 16 may be used to form the gradiometer 10, and that the gradiometer 10 may have any of several geometric configurations. However, the gradiometer 10 may not be configured to place the magnetometers 12, 14, 16 colinearly, e.g., arranged to lie along the same line.
In the exemplary embodiment, the gradient tensor component ∂Bx/∂x is estimated by taking its finite-difference approximation given by the formula [14Bx−12Bx]/L. Similarly, the five independent tensor gradient components are determined as follows:Gxx=∂Bx/∂x˜[14Bx−12Bx]/L; Gyx=∂By/∂x˜[14By−12By]/L; Gzx=∂Bz/∂x˜[14Bz−12Bz]/L; Gyy=∂By/∂y˜[16By−(12By+14By)/2]×(2/(3)1/2)/L; andGzy=∂Bz/∂y˜[16Bz−(12Bz+14Bz)/2]×(2/(3)1/2)/L.
It should be appreciated that there may also be a sixth finite difference result equivalent to one of the five indicated above. In particular, for gradiometer 10, the sixth finite difference is given by Gxy=∂Bx/∂y˜[16Bx−(12Bx+14Bx)/2]×(2/(3)1/2)/L. It should be understood that because the tensor is symmetric, Gxy=Gyx.
Due to the traceless and symmetric features of the gradient tensor matrix, measurement of five independent tensor components can be used to completely determine the full, nine component gradient tensor. Traceless is where the sum of matrix elements on the principal diagonal of the matrix is zero. Symmetric is where the matrix elements across the diagonal are equal. To verify that a given set of gradients specifies the tensor, two gradients should be diagonal terms of the 3×3 matrix and the other three should be off-diagonal terms on one side of the diagonal. It should be understood that the three off diagonal terms should not include a pair of the form ∂Bj/∂xi and ∂Bi/∂xj because such two are redundant. An example of such a pair is Gxy and Gyx. In the exemplary embodiment, the two diagonal terms are Gxx and Gyy, and the three off diagonal terms on one side of the diagonal are Gyx, Gzx, and Gzy. The gradiometer 10 measures the magnetic field as well as the gradients. Any one of the magnetometers 12, 14, 16 of the gradiometer 10 also determines a measured magnetic field. The magnetic field components at the centroid 18 of the gradiometer 10 can be approximated as Bi˜[12Bi+14Bi+16Bi]/3, where i=x,y,z.
As discussed previously, in the exemplary embodiment the ambient magnetic field is simply that of the earth, although in other various exemplary embodiments the ambient magnetic field may be an artificially generated field or that of the sun or another planet. FIG. 3 generally shows a dipole magnetic field where the circle at the center represents the size of the source, relative to the scale of the magnetic field structure. Where the source is the earth 20, its magnetic field 22 is generally smoothly varying and the scale length of those variations, of the order of the distance from the surface to the center of the earth 20, is huge compared to the gradiometer 10, so gradients associated with the earth's field 22 are very small.
FIG. 4 shows an unexploded artillery shell or unexploded ordnance (UXO) 24 and its dipole magnetic field 26 disposed in a location 28. In the exemplary embodiment the UXO 24 is located in a firing range 28. Artillery shells are made from steel which has a large magnetic permeability. The steel's large magnetic permeability concentrates the earth's magnetic field 22 inside the artillery shell steel, so that a dipole magnetic field 26 forms a local dipole magnetic field perturbation that is superimposed on the ambient magnetic field 22 of the earth 20. Because the artillery shell is small and close, relative to the center of the earth, to the gradiometer 10, the magnetic field gradients of the artillery shell 24 as well as the artillery shell's magnetic field 26 can be of appreciable magnitude. The gradiometer 10 senses the magnetic field gradients and magnetic field perturbations of the unexploded artillery shell 24 and of the unexploded artillery shell's magnetic field 26. In the exemplary embodiment, the buried artillery shell's magnetic field 26 penetrates the soil and extends above the surface of the firing range 28 largely unaffected by the soil. However, where the soil has an unusually high ferrous content, the soil has an inherent magnetic permeability which distorts the artillery shell's magnetic field 26, but does not prevent the magnetic field 26 from extending above the surface of the firing range 28.
There is needed a method for accurately locating and classifying unexploded ordnance by resolving the range-moment ambiguity, without imposing situation dependent constraints, and eliminating “ghost” solutions.